On the performance of binary extremal self-dual codes

Anton Malevich,Stefka Bouyuklieva,Wolfgang Willems

doi:10.3934/amc.2011.5.267

Abstract

The decoding error probability of a code $C$ measures thequality of performance when $C$ is used for error correction in data transmission.In this note we compare different types of codes with regard to the decoding errorprobability.

Highlights

From a pure mathematical point of view binary extremal self-dual codes of type II deserve particular attention
In this paper we investigate how good they perform if used for error correction in data transmission
To measure the performance we take the decoding error probability and assume that bounded distance decoding is used for correction of errors

Summary

Introduction

From a pure mathematical point of view binary extremal self-dual codes of type II deserve particular attention. They are related to unimodular even lattices, provide 5-designs, and often have interesting automorphism groups. To measure the performance we take the decoding error probability and assume that bounded distance decoding is used for correction of errors. A binary self-dual code C is called of type II if for all codewords c ∈ C the weight wt(c) is divisible by 4. A binary self-dual code of length n and minimum distance d satisfies n d≤4. If 24 | n an extremal self-dual code is always of type II as Rains has shown in [11]. Binary self-dual extremal codes, decoding error probabilities

Decoding error probabilities

Self-dual codes vs non self-dual codes

Experimental results

The shadow of self-dual codes

The performance of extremal self-dual codes of type I

Type I codes with minimal shadow vs type II codes